Homework 11

[Carla Nunes]

Hi,

 

Have you guys done HW11 yet?  The models I came up w/ are below.  I was wondering if anybody got the same.  I thought of checking before proceeding w/ answering the questions.

 

For VC:

	Coefficients
Intercept	1.70364398
LNQ	0.889101451
LNPM	0.832783229
LNV	-0.349329778

 

For AVC:

	Coefficients
Intercept	1.673462891
LNPM	0.834465699
LNV	-0.418656867

 

Thx,

Carla

[David Song]

Carla, 

Seems you also added Cumulative Quantity right?  because the problem states 1015 units have been produced already when these data starts.  I got same intercept and coefficients as yours.

david

[Carla Nunes]

That's correct, David.  I added the V, which is the cumulative qty.  Good to hear that u got the same!

Thanks!

Sent from my iPhone

[Spencer Hsu]

How do you determine if there is a scale or learning economies?

On Thu, Mar 3, 2011 at 5:41 PM, Carla Nunes <ccrn...@gmail.com> wrote:

[alex smirnov]

My understanding from the TA session, is that you look at your equation (Q is the only "measurement variable"):

VC=bQ^a*.    =>  

If a<1, then you have a scale economy (cost doesn't increase as fast as quantity)

If a>1, then you have a scale diseconomy (cost increasing more than quantity).  

(see slide #17) of "Cost for business decisions)

this somewhat puts things together:

http://www.mhhe.com/economics/mcconnell15e/graphics/mcconnell15eco/common/dothemath/marginalandaverageproduct.html

___________________________

Still struggling with Learning economies.  I know you do something similar with "V" (cumulative production volume), but still unclear how to exactly do it

[Sam]

My model is different than what you posted above. I included a dummy
variable I called "breakdown" which is 1 for week 21 and 0 the rest of
the time to account for the equipment failure.

For VC:
ln(VC) = -2.95 - 0.0397ln(Q) + 0.0257ln(PM) + 4.82ln(V) +
0.0027(Breakdown)

or

VC = 0.052 + Q^(-0.0397) + PM^(0.0257) + V^(4.82) + 1.003(Breakdown)

For AVC:
ln(AVC) = -1.684 - 0.3124ln (PM) – 0.5098ln (V) + 0.0125(Breakdown)

or

AVC = 5.39 + PM^(-0.3124) + V^(-0.5098) + 1.013(Breakdown)

Am I on the wrong track?

On Mar 6, 8:43 am, alex smirnov <alex.smir...@gmail.com> wrote:
> My understanding from the TA session, is that you look at your equation (Q
> is the only "measurement variable"):
>
> VC=bQ^a*.    =>
>
> If a<1, then you have a scale economy (cost doesn't increase as fast as
> quantity)

> If a>1, then you have a scale *dis*economy (cost increasing more than

> quantity).
>
> (see slide #17) of "Cost for business decisions)
>
> this somewhat puts things together:
>

> http://www.mhhe.com/economics/mcconnell15e/graphics/mcconnell15eco/co...

> ___________________________
>
> Still struggling with Learning economies.  I know you do something similar
> with "V" (cumulative production volume), but still unclear how to exactly do
> it
>

> On Sat, Mar 5, 2011 at 8:29 PM, Spencer Hsu <sphs...@gmail.com> wrote:
> > How do you determine if there is a scale or learning economies?
>

> > On Thu, Mar 3, 2011 at 5:41 PM, Carla Nunes <ccrnu...@gmail.com> wrote:
>
> >> Hi,
>
> >> Have you guys done HW11 yet?  The models I came up w/ are below.  I was
> >> wondering if anybody got the same.  I thought of checking before proceeding
> >> w/ answering the questions.
>
> >> For VC:

> >>     * *
> >>  *Coefficients*

> >>  Intercept
> >>  1.70364398
> >>  LNQ
> >>  0.889101451
> >>  LNPM
> >>  0.832783229
> >>  LNV
> >>  -0.349329778
>
> >> For AVC:

> >>     * * *Coefficients*  Intercept 1.673462891 LNPM 0.834465699 LNV
> >> -0.418656867
>
> >> Thx,
> >> Carla

[alex smirnov]

Are the t-stats high enough for the Breakdown to be significant?

[Sam]

Good point Alex. Nope, they are bad. t-stat for breakdown in VC is
0.868 with pvalue at 0.40. Breakdown in AVC is equally bad. I guess
I'll leave it out.

On Mar 6, 10:21 am, alex smirnov <alex.smir...@gmail.com> wrote:
> Are the t-stats high enough for the Breakdown to be significant?
>

[alex smirnov]

so, anybody got the learning economies figured out?

I got the same # as Carla

LNV    -0.349329778

How do you interpret that?

Also, anybody remember what was the right answer for the question on slide 28?  20% or 32%?  

[Sam]

Alex,

I think he clarifies on slide 29 saying that both answers are correct,
one for a small change V and the other for a large change in V.

On Mar 6, 10:33 am, alex smirnov <alex.smir...@gmail.com> wrote:
> so, anybody got the learning economies figured out?
>
> I got the same # as Carla
>
> LNV    -0.349329778
>
> How do you interpret that?
>
> Also, anybody remember what was the right answer for the question on slide
> 28?  20% or 32%?
>

[Sam]

My best answer so far for learning economies is:

Since EVC,V < 0, this tells us that the variable cost of production
with respect to total volume produced decreases, meaning that there is
learning. This is further affirmed since EVC,Q and EVC,PM are both
greater than 0.

Focusing just on the Evc,v seemed to be his big problem with the
Boston Consulting Group model, so I think I am missing something in my
explanation.

[Carla Nunes]

Hi guys,

 

What I have for economies of scale is what Alex has included earlier in this thread: since Evc,q < 1, we have scale economy.

Now, my understanding for learning economies is similar to the previous one, except that we look for the elasticity w/ regards to volume.  So, if Evc,v < 1, then we have learning economies.  But I'm not sure if this is correct.  :(

 

Also, based on the two models that I obtained, when I answer q3, there is inconsistency related to scale economies.  The AVC function does NOT depend on Q, so Evc,q = 0, and therefore there is NO scale economy.  Does anyone know why these answers would be different?

 

Does that mean that the model is wrong???

 

Carla

[David Song]

I'm a bit confused on Question 3: AVC function. Do we run another
regression or it can be derived as shown in Equation 6.3 on p. 226 of
the textbook?

[alex smirnov]

I don't have the same version of the book, but I believe you are supposed to run another regression

[Kevin]

I think I'm on the totally wrong track here...

for my regression I have

ln(VC) as my Y

then

ln(q)
ln(pm)
ln(v)

for the cumulative part i add 1015 to week 11 correct vc and then run
the regression?

[Carla Nunes]

That seems correct, Kevin.  Only one thing... for the Volume column, you have to calculate them first before you do the LN.  Make sure that V11 = 1015 + Q11, then V12 = V11 + Q12, V13 = V12 + Q13, etc...

You should end up w/ these for the Volumn column, which you then take the LN.

 

1127
1251
1367
1468
1593
1727
1876
2044
2221
2399
2588
2780
2966
3168
3376
3580

Hope that helps.

[Adi Aloni]

Sorry to take you back a few steps, but assuming I have the same regression results, how does the actual cost function look like?

I assume it is as follows, please correct me if I’m wrong…

 

Total Var Cost = 5.5 x Q^2.4 x PM^2.3 x V^0.7

 

Avg Var Cost = 5.3 x PM^2.3 x V^0.66

 

Thanks,

Adi.

[Kevin]

Thanks Carla. I was adding the VC not the Q.



Kevin

[Gabriel Bowers]

I've spent some time looking at #2 and #3. 

 

I can approach this problem in a similar way to the first question on the midterm seeing that the long-linear regression equation is:

ln(VC) = ln(a) + Evc,q*ln(q) + Evc,v*ln(v) + Evc,mp*ln(Mp)

 

For economies of scale I could derive:

ln(VC) = ln(a+z) + Evc,q*ln(q) --- where z = Evc,v*ln(v) + Evc,mp*ln(Mp)

Then identifying VC for two points with different Q, I could see if AVC changed when Q changed. 

 

Week #11 where Q = 112 and week #22 where Q = 204:

VC	28.9152
AVC	0.258171
VC	33.17368
AVC	0.265389

 

The fact that AVC did not change with ~100% increase in Q indicated that Evc,q may be zero.

 

I sent an email to Yang.  I may be looking too far into what may be a simple question though...

 

Gabriel

[Carla Nunes]

Hey guys,

 

I sent email to TA about question 2. 

 

For #2, we have to answer based on the VC function.  This is what she said: "When judging if there is economy of scale based on VC function, you have to decide whether 0.88910 is statistically different from 1."

 

So, you have to calculate the t-test for the coefficient of Q (0.88910) using this:  (coefficient - 1)/ std error, which in my case is:  (0.8891 - 1) / 0.1135 = -0.97.  You're here testing the null hypothesis that the coefficient = 1.  Now, I don't know if I'm supposed to compare this t w/ the "regular t-critical" of the regression, which for me is 2.17.  If that's the case, I would have to say that the coefficifient is statistically different than 1 (because 0.97 < 2.17)... but then what?  According to her, this would signify that there is constant returns to scale.  I thought it was the opposite.  If the coefficient was 1, then we would have constant returns to scale.

 

So, I'm waiting for her to reply.

 

As far as the learning economies, you only need to check the Evc,v, which is < 1, so there are learning economies.

[Carla Nunes]

Adi,

 

Your function is obtained the same way we did for the beef case in the log-linear case. 

 

Considering that you have the same regression I had, you end up w/ this:

 

VC = 5.493931* Q^0.889101451 * PM^0.832783229 * V^{- 0.349329778}

AVC = 5.330595143 * PM^0.834465699 * V^{- 0.418656867} 

Carla

[alex smirnov]

Hi Carla,

In regards to "  According to her, this would signify that there is constant returns to scale"

I think it makes sense.  Your Null Hypothesis is H0=1.  Because your t-value is < t-critical, you cannot reject H0 (H0=1), therefore you assume the coefficient you are testing is not different from 1, and therefore indicates constant returns to scale

for Evc, doesn't it have to be  -1 < Evc < 0 to indicate learning economies?  Isn't yours -.34?

[alex smirnov]

I think you are looking too far, Gabe  ;)

On Mon, Mar 7, 2011 at 12:03 AM, Gabriel Bowers <gabrie...@gmail.com> wrote:

[Gabriel Bowers]

Yes. The TA wrote back and said that I was looking too far. :-)

She confirmed Carla's approach for Ho=1.

Gabriel

On 3/7/11, alex smirnov <alex.s...@gmail.com> wrote:
> I think you are looking too far, Gabe ;)
>
>
>
> On Mon, Mar 7, 2011 at 12:03 AM, Gabriel Bowers
> <gabrie...@gmail.com>wrote:
>
>> I've spent some time looking at #2 and #3.
>>
>> I can approach this problem in a similar way to the first question on the
>> midterm seeing that the long-linear regression equation is:
>> ln(VC) = ln(a) + Evc,q*ln(q) + Evc,v*ln(v) + Evc,mp*ln(Mp)
>>
>> For economies of scale I could derive:
>> ln(VC) = ln(a+z) + Evc,q*ln(q) --- where z = Evc,v*ln(v) + Evc,mp*ln(Mp)
>> Then identifying VC for two points with different Q, I could see if AVC
>> changed when Q changed.
>>
>> Week #11 where Q = 112 and week #22 where Q = 204:
>> VC 28.9152 AVC 0.258171 VC 33.17368 AVC 0.265389
>>
>> The fact that AVC did not change with ~100% increase in Q indicated that
>> Evc,q may be zero.
>>

>> I sent an email to Yang. I may be looking *too far* into what may be a

--
Sent from my mobile device

[Adi Aloni]

Thanks Carla.

Did you consider giving paid tutoring sessions? It's gonna be a hit :)

-----Original Message-----
From: econ_401_w...@googlegroups.com
[mailto:econ_401_w...@googlegroups.com] On Behalf Of Gabriel Bowers
Sent: Monday, March 07, 2011 8:54 AM
To: alex smirnov; econ_401_w...@googlegroups.com
Subject: Re: Homework 11

[Carla Nunes]

Adi, are you joining forces w/ Alex now?  ;)

 

 

BTW, here is the rest of the values I got for the other answers.

 

3.

AVC = 5.330595143 * PM^0.834465699 * V^{- 0.418656867} 

Yes, they are consistent.  Eavc,q = 0, which implies CRS.

4.

After 5000, AVC = 0.150722578

After 1000, AVC = 0.112758079

 

5. 

No impact on the production cost.  The t-stat of the dummy variable was not statistically different than zero.

 

6.

Since there is constant returns on scale (E_{AVC, Q} = 0), average variable cost and marginal cost will be same.  Then you only need the graph for AVC and VC.

I picked values for Q varying from 1,2, ... 16 (used the same number of entries as the initial data).  Then calculated the volume starting from 2000, and starting from 5000.  Later plugged in those values in the equations obtained, and graphed the data. 

 

Hope it helps!

Carla

[Adi Aloni]

Carla, why did you use (coefficient-1) for the t test and not the coefficient itself?

 

From: econ_401_w...@googlegroups.com [mailto:econ_401_w...@googlegroups.com] On Behalf Of Carla Nunes
Sent: Monday, March 07, 2011 9:49 AM
To: econ_401_w...@googlegroups.com
Subject: Re: Homework 11

 

Adi, are you joining forces w/ Alex now?  ;)

 

 

BTW, here is the rest of the values I got for the other answers.

 

3.

AVC = 5.330595143 * PM^0.834465699 * V^{- 0.418656867}        

            Yes, they are consistent. Eavc,q = 0, which implies CRS.

            4.

            After 5000,AVC = 0.150722578

[Adi Aloni]

I agree with Alex.

When we do hypothesis testing, we’re trying to reject the null hypothesis. A t-stat of 0.97 means we cannot reject H0, as Alex said. In this case, it means there are no scale economies, or constant returns to scale.

However, I don’t understand why we calculate the t-stat as we did.

 

For the average cost, when I run the regression with Q in it, the coefficient for Q is -0.11 with a p-value of 0.347. this p-value means that this coefficient is not statistically different from zero, and this is consistent with no scale economies. If there were scale economies, Q had to be also in the average cost function.

[alex smirnov]

Adi,

the formula for t-stat, is always (coefficient-H0)/std error.  H0 is usually 0, and is the default in excel

the TA said that for VC only, you are trying to judge if the coefficient is statistically different from "1", not "0", that's why you subtract "1"

[Carla Nunes]

Ditto very well by Alex.  He was the one who helped me understand the non-rejection of H0.  I got it all confused at the beginning.

[Carla Nunes]

Not my approach!  I asked her too.  :)  And Alex helped w/ that!  ;P

[alex smirnov]

I absolve myself of all responsibility for that.  I think it should forever be known as Carla's approach  =)

[Savita Raina]

Thanks Carla, Alex, Adi, Gabriel, David, Sam and other if i missed mentioning for contributing to the class.

 

Just an explaination for t-stat, hope it helps

 

In general t stat  = (x bar) - ud / sd / sqrt n

 

x bar is the sample mean

ud = is the specified value to be tested (in this case it is 1)

sd is the sample standard deviation, and n is the size of the sample

 

Savita

 

 

On Mon, Mar 7, 2011 at 10:20 AM, alex smirnov <alex.s...@gmail.com> wrote:

[Kevin]

I'm seeing different cost functions. Can anyone explain why there are
different types? Is there more than one? How do I know which to use?

Carla,

I got the same co-efficients as you, however I don't understand in
your cost function the first co-efficient becomes 5.49391.



Kevin

On Mar 7, 8:14 am, Carla Nunes <ccrnu...@gmail.com> wrote:
> Adi,
>
> Your function is obtained the same way we did for the beef case in the
> log-linear case.
>
> Considering that you have the same regression I had, you end up w/ this:
>
> VC = 5.493931* Q0.889101451 * PM0.832783229 * V- 0.349329778
>
> AVC = 5.330595143 * PM0.834465699 * V- 0.418656867
>
> Carla
>
>
>
>
>
>
>
> On Sun, Mar 6, 2011 at 10:22 PM, Adi Aloni <aloni....@gmail.com> wrote:
> >  Sorry to take you back a few steps, but assuming I have the same
> > regression results, how does the actual cost function look like?
>
> > I assume it is as follows, please correct me if I’m wrong…
>
> > Total Var Cost = 5.5 x Q^2.4 x PM^2.3 x V^0.7
>
> > Avg Var Cost = 5.3 x PM^2.3 x V^0.66
>
> > Thanks,
>
> > Adi.
>

> > *From:* econ_401_w...@googlegroups.com [mailto:
> > econ_401_w...@googlegroups.com] *On Behalf Of *Carla Nunes
> > *Sent:* Sunday, March 06, 2011 10:09 PM
> > *To:* econ_401_w...@googlegroups.com
> > *Subject:* Re: Homework 11

>
> > That seems correct, Kevin.  Only one thing... for the Volume column, you
> > have to calculate them first before you do the LN.  Make sure that V11 =
> > 1015 + Q11, then V12 = V11 + Q12, V13 = V12 + Q13, etc...
>
> > You should end up w/ these for the Volumn column, which you then take the
> > LN.
>
> > 1127
>
> > 1251
>
> > 1367
>
> > 1468
>
> > 1593
>
> > 1727
>
> > 1876
>
> > 2044
>
> > 2221
>
> > 2399
>
> > 2588
>
> > 2780
>
> > 2966
>
> > 3168
>
> > 3376
>
> > 3580
>
> > Hope that helps.
>

[Carla Nunes]

Hi Kevin,

 

After u run the regression, you get the following function for VC

 

Intercept1.70364398
LNQ0.889101451
LNPM0.832783229
LNV-0.349329778

ln(VC) = 1.70 + 0.88LN(Q) + 0.83 LN(PM) - 0.34 LN(V)

then you take the exp (or inverse log)

 

you get:

 

VC = e^1.70 * Q^0.88 * PM ^ 0.83 * V ^ -0.34

VC = 5.33 * Q^0.88 * PM ^ 0.83 * V ^ -0.34

You do the same for AVC.

 

Carla

[Kevin]

Can I sign up for the Carla tutoring sessions?

[Elliott Le]

Hi Carla,

Can you explain a bit more as how you graphed AVC for Q#5?

Thanks,

Elliott Le

--
Elliott Le

[Spencer]

Carla should just take over on Saturday's.

Sent from my iPhone

[Elliott Le]

Oops, just realized how it's done.

Elliott Le

--
Elliott Le

[Xiuya Li]

Hi Carla,

 

I got the same of VC with yours, but for AVC, can you please explain why you left out Q? I think Q should be there because you are comparing coefficient of Q (-0.11) with 1, which is far away from 1, so there exists scale of economy (not like in VC case, coefficent of Q is close to 1, so no scale of economies).

 

I used t=(-0.11-1)/0.11 > 10, so you can not ignore Q (reject H0, not using the P-Value from regression because that's based on H0=0, not H0=1).

 

Am I missing something here?

 

Thanks!

Ted

On Thu, Mar 3, 2011 at 5:41 PM, Carla Nunes <ccrn...@gmail.com> wrote:

Hi,

 

Have you guys done HW11 yet?  The models I came up w/ are below.  I was wondering if anybody got the same.  I thought of checking before proceeding w/ answering the questions.

 

For VC:

	Coefficients
Intercept	1.70364398
LNQ	0.889101451
LNPM	0.832783229
LNV	-0.349329778

 

For AVC:

	Coefficients
Intercept	1.673462891
LNPM	0.834465699
LNV	-0.418656867

 

Thx,

Carla

[Carla Nunes]

Hi Ted,

 

Sorry, only now I'm seeing this msg.  :(  I was offline since 3pm today.

For the AVC function, I left out Q because when I added, it was giving me a wrong t stat in a set of combinations tried. So, I decided to remove it from the final equation.

 

Carla